High-pressure superconductivity in hexagonal CaSH₃ with a nonclathrate molecular hydrogen structure

Understanding the interplay between pressure-driven Fermi surface electronic states and phonon hardening is essential for exploring high-temperature superconducting materials. In this study, using first-principles structure searches, we identify two thermodynamically stable ternary Ca-S-H phases at 200 GPa: P6̄m2 CaSH₃ and C2/m Ca₂SH₆. Structural and bonding analyses reveal that both compounds consist of non-cage-like quasi-H₂ units formed by H-H covalent bonds, together with weak ionic interactions between Ca and S, and exhibit metallic character. Among them, CaSH₃ exhibits a superconducting transition temperature (T_c) of 82.35 K at 200 GPa. The electron-phonon coupling (EPC) is found to originate primarily from an acoustic E' mode at the L point, corresponding to out-of-plane shear vibrations of S atoms, with low- to medium-frequency phonon modes dominating the total EPC. Furthermore, pressure exerts a dual effect on T_c: on one hand, increasing pressure reduces the density of electronic states at the Fermi level, which suppresses the electron-phonon coupling; on the other hand, pressure induces phonon hardening (i.e., increased phonon frequencies), thereby enhancing T_c. This work reveals the competition between the electronic density of states and phonon hardening under high pressure, offering new insights into the superconducting mechanism of high-pressure hydrides.